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DOUBLE PRECISION FUNCTION <a name="ZLANSB.1"></a><a href="zlansb.f.html#ZLANSB.1">ZLANSB</a>( NORM, UPLO, N, K, AB, LDAB,
$ WORK )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER NORM, UPLO
INTEGER K, LDAB, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> DOUBLE PRECISION WORK( * )
COMPLEX*16 AB( LDAB, * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="ZLANSB.20"></a><a href="zlansb.f.html#ZLANSB.1">ZLANSB</a> returns the value of the one norm, or the Frobenius norm, or
</span><span class="comment">*</span><span class="comment"> the infinity norm, or the element of largest absolute value of an
</span><span class="comment">*</span><span class="comment"> n by n symmetric band matrix A, with k super-diagonals.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Description
</span><span class="comment">*</span><span class="comment"> ===========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="ZLANSB.27"></a><a href="zlansb.f.html#ZLANSB.1">ZLANSB</a> returns the value
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="ZLANSB.29"></a><a href="zlansb.f.html#ZLANSB.1">ZLANSB</a> = ( max(abs(A(i,j))), NORM = 'M' or 'm'
</span><span class="comment">*</span><span class="comment"> (
</span><span class="comment">*</span><span class="comment"> ( norm1(A), NORM = '1', 'O' or 'o'
</span><span class="comment">*</span><span class="comment"> (
</span><span class="comment">*</span><span class="comment"> ( normI(A), NORM = 'I' or 'i'
</span><span class="comment">*</span><span class="comment"> (
</span><span class="comment">*</span><span class="comment"> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> where norm1 denotes the one norm of a matrix (maximum column sum),
</span><span class="comment">*</span><span class="comment"> normI denotes the infinity norm of a matrix (maximum row sum) and
</span><span class="comment">*</span><span class="comment"> normF denotes the Frobenius norm of a matrix (square root of sum of
</span><span class="comment">*</span><span class="comment"> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> NORM (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies the value to be returned in <a name="ZLANSB.46"></a><a href="zlansb.f.html#ZLANSB.1">ZLANSB</a> as described
</span><span class="comment">*</span><span class="comment"> above.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> Specifies whether the upper or lower triangular part of the
</span><span class="comment">*</span><span class="comment"> band matrix A is supplied.
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangular part is supplied
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangular part is supplied
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix A. N >= 0. When N = 0, <a name="ZLANSB.56"></a><a href="zlansb.f.html#ZLANSB.1">ZLANSB</a> is
</span><span class="comment">*</span><span class="comment"> set to zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> K (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The number of super-diagonals or sub-diagonals of the
</span><span class="comment">*</span><span class="comment"> band matrix A. K >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> AB (input) COMPLEX*16 array, dimension (LDAB,N)
</span><span class="comment">*</span><span class="comment"> The upper or lower triangle of the symmetric band matrix A,
</span><span class="comment">*</span><span class="comment"> stored in the first K+1 rows of AB. The j-th column of A is
</span><span class="comment">*</span><span class="comment"> stored in the j-th column of the array AB as follows:
</span><span class="comment">*</span><span class="comment"> if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
</span><span class="comment">*</span><span class="comment"> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDAB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array AB. LDAB >= K+1.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
</span><span class="comment">*</span><span class="comment"> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
</span><span class="comment">*</span><span class="comment"> WORK is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> INTEGER I, J, L
DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.88"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.89"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="ZLASSQ.92"></a><a href="zlassq.f.html#ZLASSQ.1">ZLASSQ</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC ABS, MAX, MIN, SQRT
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span> IF( N.EQ.0 ) THEN
VALUE = ZERO
ELSE IF( <a name="LSAME.101"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'M'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Find max(abs(A(i,j))).
</span><span class="comment">*</span><span class="comment">
</span> VALUE = ZERO
IF( <a name="LSAME.106"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
DO 20 J = 1, N
DO 10 I = MAX( K+2-J, 1 ), K + 1
VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
10 CONTINUE
20 CONTINUE
ELSE
DO 40 J = 1, N
DO 30 I = 1, MIN( N+1-J, K+1 )
VALUE = MAX( VALUE, ABS( AB( I, J ) ) )
30 CONTINUE
40 CONTINUE
END IF
ELSE IF( ( <a name="LSAME.119"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'I'</span> ) ) .OR. ( <a name="LSAME.119"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'O'</span> ) ) .OR.
$ ( NORM.EQ.<span class="string">'1'</span> ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Find normI(A) ( = norm1(A), since A is symmetric).
</span><span class="comment">*</span><span class="comment">
</span> VALUE = ZERO
IF( <a name="LSAME.125"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
DO 60 J = 1, N
SUM = ZERO
L = K + 1 - J
DO 50 I = MAX( 1, J-K ), J - 1
ABSA = ABS( AB( L+I, J ) )
SUM = SUM + ABSA
WORK( I ) = WORK( I ) + ABSA
50 CONTINUE
WORK( J ) = SUM + ABS( AB( K+1, J ) )
60 CONTINUE
DO 70 I = 1, N
VALUE = MAX( VALUE, WORK( I ) )
70 CONTINUE
ELSE
DO 80 I = 1, N
WORK( I ) = ZERO
80 CONTINUE
DO 100 J = 1, N
SUM = WORK( J ) + ABS( AB( 1, J ) )
L = 1 - J
DO 90 I = J + 1, MIN( N, J+K )
ABSA = ABS( AB( L+I, J ) )
SUM = SUM + ABSA
WORK( I ) = WORK( I ) + ABSA
90 CONTINUE
VALUE = MAX( VALUE, SUM )
100 CONTINUE
END IF
ELSE IF( ( <a name="LSAME.154"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'F'</span> ) ) .OR. ( <a name="LSAME.154"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( NORM, <span class="string">'E'</span> ) ) ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Find normF(A).
</span><span class="comment">*</span><span class="comment">
</span> SCALE = ZERO
SUM = ONE
IF( K.GT.0 ) THEN
IF( <a name="LSAME.161"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( UPLO, <span class="string">'U'</span> ) ) THEN
DO 110 J = 2, N
CALL <a name="ZLASSQ.163"></a><a href="zlassq.f.html#ZLASSQ.1">ZLASSQ</a>( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ),
$ 1, SCALE, SUM )
110 CONTINUE
L = K + 1
ELSE
DO 120 J = 1, N - 1
CALL <a name="ZLASSQ.169"></a><a href="zlassq.f.html#ZLASSQ.1">ZLASSQ</a>( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
$ SUM )
120 CONTINUE
L = 1
END IF
SUM = 2*SUM
ELSE
L = 1
END IF
CALL <a name="ZLASSQ.178"></a><a href="zlassq.f.html#ZLASSQ.1">ZLASSQ</a>( N, AB( L, 1 ), LDAB, SCALE, SUM )
VALUE = SCALE*SQRT( SUM )
END IF
<span class="comment">*</span><span class="comment">
</span> <a name="ZLANSB.182"></a><a href="zlansb.f.html#ZLANSB.1">ZLANSB</a> = VALUE
RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> End of <a name="ZLANSB.185"></a><a href="zlansb.f.html#ZLANSB.1">ZLANSB</a>
</span><span class="comment">*</span><span class="comment">
</span> END
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